College Physics
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ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Electric Field and Sparks: A Detailed Analysis**
**Problem Statement:**
(II) An electric field greater than about \(3 \times 10^6\) V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). Refer to Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
**Solution:**
1. **Understanding the Breakdown of Air:**
- When the electric field exceeds approximately \(3 \times 10^6\) V/m, the air ionizes, and electrons are liberated from atoms, resulting in a discharge of energy as light, creating a spark.
2. **Estimating the Electric Field Gap:**
- Distance between finger and doorknob: \(d = 1 \text{ mm} = 0.001 \text{ m}\)
- Electric field causing breakdown: \(E = 3 \times 10^6 \text{ V/m}\)
3. **Calculating the Voltage:**
- Voltage (\(V\)) can be estimated using the relationship \(V = E \times d\)
- Given values:
\[
V = (3 \times 10^6 \text{ V/m}) \times (0.001 \text{ m}) = 3000 \text{ V}
\]
4. **Conclusion - Why No Harm is Done:**
- The spark is of very short duration and the amount of energy involved is relatively low.
- Human skin acts as a good insulator.
- The current involved in the spark is minimal and not enough to cause harm.
This analysis provides an estimation of the voltage that can arise in a common scenario and explains why a common static discharge, such as touching a doorknob after walking on a carpet, does not typically cause harm despite the high voltage involved.](https://content.bartleby.com/qna-images/question/a96c07fd-e70d-478a-a514-a2ec6704d773/5144cd7a-19d4-4840-835f-f8aec32893c7/gbd7nhz_processed.png)
Transcribed Image Text:**Electric Field and Sparks: A Detailed Analysis**
**Problem Statement:**
(II) An electric field greater than about \(3 \times 10^6\) V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). Refer to Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
**Solution:**
1. **Understanding the Breakdown of Air:**
- When the electric field exceeds approximately \(3 \times 10^6\) V/m, the air ionizes, and electrons are liberated from atoms, resulting in a discharge of energy as light, creating a spark.
2. **Estimating the Electric Field Gap:**
- Distance between finger and doorknob: \(d = 1 \text{ mm} = 0.001 \text{ m}\)
- Electric field causing breakdown: \(E = 3 \times 10^6 \text{ V/m}\)
3. **Calculating the Voltage:**
- Voltage (\(V\)) can be estimated using the relationship \(V = E \times d\)
- Given values:
\[
V = (3 \times 10^6 \text{ V/m}) \times (0.001 \text{ m}) = 3000 \text{ V}
\]
4. **Conclusion - Why No Harm is Done:**
- The spark is of very short duration and the amount of energy involved is relatively low.
- Human skin acts as a good insulator.
- The current involved in the spark is minimal and not enough to cause harm.
This analysis provides an estimation of the voltage that can arise in a common scenario and explains why a common static discharge, such as touching a doorknob after walking on a carpet, does not typically cause harm despite the high voltage involved.
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